In a large bowl, combine the coconut oil and light brown sugar with a spoon until well combined, with no lumps. Into the bowl, add the peanut butter, apple sauce, and vanilla and stir well to combine. Add the oats, salt and baking powder into the bowl and stir well. Don't worry about over mixing. Without gluten, over mixing isn't really possible. You want to mix this batter for a solid two minutes.
Next, cover and let the cookie dough rest on the counter for 45 minutes. This is crucial. The oats need a little time to soften and soak up liquid from the dough. If you try to shortchange this resting time, the cookies will probably fall apart on you.
Pre heat your oven to 350* F.
After the dough has rested, add in the chocolate chips and chopped peanuts and stir well once more. Scoop the dough onto a parchment lined baking sheet in 2-3 Tablespoons mounds, with the mounds being a couple inches apart from each other. The dough will look like its falling apart on you here- don't freak out. Now, wet your hands a little bit, and with damp hands, press the dough into a disc on the cookie sheet (shown above). These cookies don't spread a lot, so pretty much how you press them our is how they will look when they are baked so keep that in mind.
Bake at 350* for 15-18 minutes, turning the tray half way through. The edges will be just starting to brown. Let them cool on the baking sheets for 10 minutes before transferring to a wire cooling rack to completely cool.